And the Switch uses Vulkan; while Vulkan on top of Windows (including 7 and 8/8.1) supports Linux and Android. For iOS and macOS there's MoltenVK, but I can't speak for its quality.
https://blogs.nvidia.com/blog/2016/10/20/nintendo-switch/
So it remains to be seen which one gets the love of game developers.
That's actually a fairly interesting question, given the percentage of games that come out for Nintendo platforms which are exclusive to that platform (or at least to the Nintendo family of platforms). There are all the first party titles, and then there are all the esoteric games which don't really fit the control schemes of the other platforms (but the switch is less unique in this aspect). I imagine games targeted purely at Nintendo platforms might use their proprietary API, especially first party games, which might get the API changed based on their needs.
DirectX 12 runs on XBox One, while Vulkan does not:
> http://www.redgamingtech.com/directx-12-for-xbox-one-is-here...
And for OSX/iOS, you have to use OpenGL or Metal.